Problem: What number could replace $k$ below? $\dfrac{3}{4} = \dfrac{6}{k}$
Solution: The fraction on the left represents 3 out of 4 slices of a rectangular cake. How many total slices would we need if we want the same amount of cake in 6 slices? We would need to cut the cake into 8 slices. $\dfrac{3}{4} = \dfrac{6}{8}$ and so the answer is $8$ Another way to get the answer is to multiply by $\dfrac{2}{2}$ $\dfrac{2}{2} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{3}{4} \times \dfrac{2}{2} = \dfrac{6}{8} $ so our answer is $8$.